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1. a) Let F(x,y) = hcosy,−xsiny + 2yi. Show that F is conservative, and find a...

1. a) Let F(x,y) = hcosy,−xsiny + 2yi. Show that F is conservative, and find a function
φ such that ∇φ(x,y) = F(x,y).
b) Use the result from part a) to find
R
C F · Tds, where C is given by r(t) = ht,πti,0 ≤
t ≤ 1.

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